Holomorphic quadratic differentials in Teichmüller theory

Gupta, Subhojoy

doi:10.4171/203-1/4

Cited by 3 publications

(1 citation statement)

References 110 publications

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“…The space Q(S) further carries a natural stratification depending on the order of the zeroes of q. Please consult, for example [22], [18], [21] for references on this topic.…”

Section: Q(s) and Foliations Realised By Holomorphic Quadratic Differ...mentioning

confidence: 99%

Measured foliations at infinity of quasi-Fuchsian manifolds near the Fuchsian locus

Choudhury¹

2021

Preprint

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Given a pair of measured foliations (F + , F − ) which fill a closed hyperbolic surface S, we show that for t > 0 sufficiently small, tF + and tF − can be uniquely realised as the measured foliations at infinity of a quasi-Fuchsian hyperbolic 3-manifold homeomorphic to S × R, which is in a suitably small neighbourhood of the Fuchsian locus. This is parallel to a theorem of Bonahon that partially answers a conjecture of Thurston by proving that a quasi-Fuchsian manifold close to being Fuchsian can be uniquely determined by the data of measured bending laminations on the boundary of its convex core. We also give an interpretation of our result in half-pipe geometry using intermediate steps in the proof.

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“…The space Q(S) further carries a natural stratification depending on the order of the zeroes of q. Please consult, for example [22], [18], [21] for references on this topic.…”

Section: Q(s) and Foliations Realised By Holomorphic Quadratic Differ...mentioning

confidence: 99%

Measured foliations at infinity of quasi-Fuchsian manifolds near the Fuchsian locus

Choudhury¹

2021

Preprint

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Compactification and distance on Teichmüller space via renormalized volume

MASAI

2024

J. Math. Soc. Japan

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Compactification and distance on Teichmüller space via renormalized volume

Masai¹

2021

Preprint

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We introduce a variant of horocompactification which takes "directions" into account. As an application, we construct a compactification of the Teichmüller spaces via the renormalized volume of quasi-Fuchsian manifolds. Although we observe that the renormalized volume itself does not give a distance, the compactification allows us to define a new distance on the Teichmüller space. We show that the translation length of pseudo-Anosov mapping classes with respect to this new distance is precisely the hyperbolic volume of their mapping tori. A similar compactification via the Weil-Petersson metric is also discussed.

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Holomorphic quadratic differentials in Teichmüller theory

Cited by 3 publications

References 110 publications

Measured foliations at infinity of quasi-Fuchsian manifolds near the Fuchsian locus

Measured foliations at infinity of quasi-Fuchsian manifolds near the Fuchsian locus

Compactification and distance on Teichmüller space via renormalized volume

Compactification and distance on Teichmüller space via renormalized volume

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